Calculus of Variations and Geometric Measure Theory
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Rank-one convex functions which are 1-homogeneous

Bernd Kirchheim

created by magnani on 08 Mar 2013

13 mar 2013 -- 18:00   [open in google calendar]

Sala Seminari, Department of Mathematics, Pisa University

Abstract.

Vectorial problems in the Calculus of Variations are naturally related to generalized notions of convexity - which for instance characterize weak lower semicontinuity locally or globally. In the past, mainly the differences between these notions were investigated. Here we present a result which shows that for one-homogeneus functions all these possible convexity notions agree in the best possible way.

This result, obtained jointly with Jan Kristensen, also allows to put Ornstein's famous L-one non-inequality as well as similar constructions by Conti, Faraco, Maggi and Mueller into a unifying frame and to generalize them.

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